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The Bogomolv theorem holds great importance in algebraic geometry, particularly in the field of birational geometry. During this presentation, we will introduce our recent work on a variant of the Bog...
I will first give a brief introduction to T. Mochizuki's Theory of twistor D-modules. Then, we use it to study Kodaira-type vanishings. In particular, we will generalize Saito vanishing, and give a Ka...
In these two talks, some results on derived representation type via topological and homological methods will be introduced: (1) Two geometric models for graded skew-gentle algebras will be introduced ...
In these two talks, some results on derived representation type via topological and homological methods will be introduced: (1) Two geometric models for graded skew-gentle algebras will be introduced ...
Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geom...
We propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of ...
Invariant geometric flows in certain geometries have been studied extensively from different points of view. In this talk, we are mainly concerned with geometric aspects of multi-component integrable ...
The theory of tetragonal curves is established and first applied to the study of algebro-geometric quasi-periodic solutions of discrete soliton equations. Using the zero-curvature equation and the dis...
In this talk, I will explain the relationship between the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces and the existence of Shokurov polytopes. For K3 fibrations, this enables us to e...
In this talk I will introduce special and generalized cycles on Shimura varieties and discuss how to use them to construct geometric and arithmetic theta series. Then I will briefly discuss the connec...
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
“Superparamagnetic limit”: As magnetic devices become smaller and smaller, the time for thermal activated switching might become too short (shorter than desired data retention time).
A curve C in the projective plane is called non-negative if the self-intersection number of C after the minimal resolution of singularities of C is non-negative. Given a unicuspidal rational plane cur...
Abstract: We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system ...
Abstract: The authors construct the global Macaulay inverse system for a zero-dimensional subscheme Z of projective n-space P^n, from the local inverse systems of the irreducible components of Z. This...

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